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Wednesday, 15 August 2012

Multiplication and mental maps

On Monday night, Michael Rosen triggered a twitter debate about the pros and cons of children learning what is traditionally referred to as 'times tables' - i.e. being able to instantly recall basic multiplication in your head - in primary schools. This was prompted by wider public debate about proposed changes to the primary maths curriculum.

Michael then posted a series of contributions by some of us who had commented on twitter, as a chance to develop our thoughts in more detail than 140 characters. My contribution - see an only slightly edited version below - was responding to those who suggested that times tables don't matter.

The current proposals for reform of the primary maths curriculum appear
to be yet another strand in Michael Gove's ideological assault on learning. As
with the 'facts, facts, facts' approach to history teaching, it seems to be a
case of treating learning as merely a series of boxes to tick: specific items of
knowledge, separated from each other. It runs contrary to more egalitarian
notions of learning, which grasp the complexity of learning and focus on
conceptual development: making connections, understanding and applying concepts,
developing higher levels of thinking.

The government's latest is also
part of the obsessive teacher-blaming and determination to distract us from the
real (political and economic) causes of high unemployment and poverty that we
expect from the Tories.

But opposition to Gove's ideology should not mean
rejecting the notion of multiplication tables as a core understanding. Indeed
they are valuable to conceptual development. They are not simply a discrete
factual topic (like, say, learning the names of the world's capital
cities - a mistaken analogy which someone offered on Twitter).

We should reject the absurdly prescriptive approach of demanding
that ALL children must know their times tables by a certain age - why nine years
old anyway? where does that come from? - and reject the framing of times tables
as one of a series of 'basic skills' like spelling that are given a reified
status. Actually, they are cognitively very different to spelling - for example,
learning how to spell is all about developing a grasp of both patterns and
variations (and one aspect of developing competence in writing), whereas times
tables are finite and clearly defined. Put bluntly: you just have to learn the
buggers.

Can someone be good at Maths, go on to study the subject at
university, etc, without being able to do basic multiplication mentally? No doubt they can. This
isn't about the subject of Maths - though I can't help thinking that any Maths
student would benefit from memorising times tables, considering how valuable
they are for arithmetic. No - it is about recognising a very useful building
block in conceptual understanding.

People sometimes say 'But when do I
ever need to use times tables in everyday life?' If we apply such a narrow,
reductive utilitarian logic there is little point in ever learning anything. In
an age when you can look pretty much anything up on Wikipedia, why learn
anything so that you can 'use' it?

The point is that - once mentally embedded -
a grasp of basic multiplication becomes part of how we comprehend the world
(along with a whole bunch of other skills, concepts and understandings - let's
ditch the sacred halo here). It is part of what might loosely be
termed a mental map of the world.

During the Olympics I spent far too
many hours tuned into TV coverage or listening to Radio 5 Live. During those
many hours I must have done mental arithmetic literally hundreds of times:
calculating, comparing, estimating and evaluating speeds, distances, scores etc. Of course you can live without
that kind of capacity for arithmetic, but it illustrates the point that we
actually use arithmetic all the time, even if not consciously aware that we're
doing so. Every time I go shopping, every time I use a cash machine, every time
I buy a drink in a bar, every time I check a utility bill... you get the
idea.

Being able to multiply quickly, and without paper or technology, is
not the be-all and end-all. It shouldn't be given a reified status or be
presented to children as an obstacle over which they must jump before proceeding
any further. It shouldn't be taught in such a way that children feel a failure
if it takes them longer than some of their classmates to learn. Comparing and
ranking should be avoided, and artificially prescriptive age 'targets' don't
help.

But none of that should distract from the valuable place that
mutiplication tables do have in intellectual development - in helping with a
capacity for sequencing, calculating, comparing, estimating etc, as part of the foundations
for further numeracy development, as what could become an embedded part of
someone's mental map for life.